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Full text of "Analytical Mechanics"

the pitch and the direction of the axis of the screw-motion change from instant to instant. In the case of the motion of a screw in its nut these do not change.
Translation and rotation are special cases of screw-motion. When the pitch of a screw is made smaller and smaller it advances less and less during each revolution. Therefore if the pitch is made to vanish the screw does not advance at all when it is rotated. Thus rotation is a special case of screw-motion in which the pitch is zero. On the other hand as the pitch of the screw is made greater and greater the screw advances more and more during each revolution. Therefore at the limit when the pitch is infinitely great the motion of the screw becomes a motion of translation. Thus translation is a special case of screw-motion in which the pitch is infinitely great.
40.   Two Types of Action.™—We have seen that a rigid body may have two different and independent types of motion, namely,  motion of  translation and  motion  of  rotation. These motions  are  the  results  of two  independent  and entirely different kinds of actions to which a rigid body is capable of being subjected.    We will differentiate between these two types of action by adding the adjectives "linear" and "angular" to the term *'action."   Thus the action which tends to produce translation will be called linear action and that which tends to produce rotation, angular action.
41.   Torque.—The vector magnitude which represents the angular action of one body upon another is called torque.
42.   Couple.— Although a single force is not capable of giving a rigid body a motion of pure rotation, two or more external forces will  do it when  properly applied.     The simplest system of forces which is capable of producing rotation is known as a couple.   It consists of two equal and opposite forces which are not in the same line, Fig. 26.